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Abstract
Abstract Conventional analysis of cake filtration considers cakes formed under one-dimensional rectilinear flow conditions. Other cake geometries are often encountered in practice, and more generalized equations are needed. An orthogonal curvilinear filter cake equation is derived here for an arbitrary orthogonal cake geometry. This equation is applied to rectangular, cylindrical, oblate-spheroidal, and elliptic-cylindrical geometry cakes through the coordinate scale factors. Experiments are run on Lucite cakes in rectangular and elliptic-cylindrical coordinates. The constitutive parameter, Λ, is determined from experiments in rectangular coordinates and is used to predict the performance of an elliptic-cylindrical cake. Comparison of the predicted results with the experimental results of the elliptic-cylindrical cake shows the consistency of the equation for different geometries. The filter assembly used in the experiments was designed to be pressurized without being submerged within a larger slurry agit...
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